Emerging from its first election with a string of major victories – and two glaring defeats – leaders of the tea party movement wasted no time claiming credit and taking names, signaling to the Republican establishment that they intend to remake the GOP, not merely help it regain power in Washington.

“Tonight, there’s a tea party tidal wave, and we’re sending a message to them!” tea party favorite Rand Paul proclaimed after being declared the winner of the Kentucky Senate race on Tuesday.

The message he said he would deliver to the Senate, which he called “the world’s most deliberative body,” is “to deliberate upon this: The American people are unhappy with what’s going on in Washington” and have “come to take our government back!”

But many tea party organizers cautioned that the nascent movement has perhaps its toughest challenges ahead of it in keeping activists engaged and newly elected champions true to the small government principles of the movement. And, as usual in the diffuse and decentralized movement, there are sharp differences about how to proceed.

But such concerns were secondary Wednesday morning as organizers savored the role the anti-establishment grassroots uprising – borne less than two years ago – had played in reclaiming the House of Representatives for the GOP.

And while there was some hand-wringing over the fact that the defeat of two of the tea party’s most high profile candidates, Sharron Angle in Nevada and Christine O’Donnell in Delaware, helped keep Republicans from also taking the Senate, tea party organizers said the GOP wouldn’t have even have been within striking distance had it not been for the movement.

“We succeeded far beyond what anybody would have predicted. We’ve completely changed the complexion of American politics,” said Sal Russo, a veteran GOP operative who founded the Tea Party Express political action committee, which played a critical role in securing the GOP nominations for Angle, O’Donnell, and Joe Miller of Alaska, whose race has not been decided.

“I’m satisfied with our candidates,” he said. “They were right on the issues and in concert with the zeitgeist of our times.”

He and other key tea party organizers are already looking ahead to the 2012 presidential race (with Russo signaling a preference for Sarah Palin), and also plotting primary challenges against Republican lawmakers deemed to be out of step with the movement’s small government principles.

Oft-cited targets include incumbent Sens. Orrin Hatch of Utah, Kay Bailey Hutchison of Texas, Olympia Snowe of Maine and Roger Wicker of Mississippi and any newly elected House Republicans deemed to have departed from pledges to adhere to tea party principles.

Other tea party leaders were relishing roles as behind-the-scenes players in the new Congress.

“The fact of the matter is most of the most prominent people in the Senate have within the past four months been in touch with me to try to figure out ways in which we can have a better working relationship,” former House Majority Leader Dick Armey, who chairs the small government tea party group FreedomWorks, told POLITICO as election results rolled in late Tuesday. “Now, do you think that’s because I’m such a handsome fella?”

“I think it’s because I’m seen as a liaison to the tea party. And (lawmakers) are saying ‘you know, these folks are carrying a pretty big influence across this country and I sure want them to love me.’ So all of a sudden, I’m a matchmaker,” said Armey, whose group was among the earliest national supporters of victorious tea party Senate candidates Marco Rubio of Florida and Mike Lee of Utah, as well as of Ken Buck of Colorado, who was locked in a tight contest early Wednesday.

In addition to Paul, Lee and Rubio, tea party favorites Pat Toomey of Pennsylvania and Ron Johnson of Wisconsin also won hotly contested Senate seats, while several incumbent House Democrats were ousted by Republicans who had identified as tea partiers, including Allen West of Florida and Scott Rigell and Morgan Griffith of Virginia.

Sen. Jim DeMint (R-S.C.), a tea party hero who had angered his own caucus by backing tea party candidates over establishment Republicans in primaries, predicted that incoming tea party supporters will be under heavy pressure to put GOP interests before tea party principles.

“The establishment is much more likely to try to buy off your votes than to buy into your limited-government philosophy,” DeMint, who cruised to an easy reelection win, wrote in the Wall Street Journal.

“Tea party Republicans were elected to go to Washington and save the country—not be co-opted by the club,” wrote DeMint, who is expected to emerge as the leader an unofficial Senate tea party caucus. “So put on your boxing gloves. The fight begins today.”

DeMint urged the incoming tea party class not to seek earmarks, positions with fancy titles or committee assignments that “can be used as bait to make senators compromise on other matters.”

He also warned them not to “let your re-election become more important than your job. ... People will try to convince you to moderate conservative positions and break campaign promises, all in the name of winning the next race. Resist the temptation to do so.”

DeMint is expected to lead an early test of Senate tea party power by trying again toban the body from earmarking. But DeMint spokesman Matt Hoskins dismissed a suggestion that DeMint expects support from his tea party cohorts or that he’s angling to lead them in a tea party insurrection against Senate Minority Leader Mitch McConnell (R-Ky.), who backed establishment candidates defeated by DeMint’s tea party challengers.

“His focus is going to be working to make sure that they’re successful,” Hoskins told POLITICO.

But in the House, a handful of newly elected members who won with tea party backing – including Kristi Noem of South Dakota, Bill Flores of Texas and Rigell of Virginia – along with Rep. Michele Bachmann of Minnesota, have suggested they might be willing to support a conservative challenge to the likely bid for House Speaker by veteran insider Rep. John Boehner (R-Ohio).

Tea partiers for months have angrily pointed to a July comment from former Senate GOP leader Trent Lott about Republicans needing “to co-opt” tea party lawmakers “as soon as they get here” because “We don’t need a lot of Jim DeMint disciples.”

McConnell late last month expressed a similar sentiment – albeit more diplomatically – about the need for GOP leaders to do a lot of “preaching and teaching” with tea party newcomers.

“One of the things we will have to remind newcomers and those who have supported them is that even though we will have a larger Republican Conference, we do not control the government and cannot control the government when the president holds the veto pen,” McConnell told National Journal.

There’s not going to be patience for that among tea party activists, according to Adam Brandon, spokesman for FreedomWorks, which pushed its candidates to sign a crowd-sourced statement of tea party policy positions called the Contract from America.

“We’re going to be reminding people that we were not joking about that contract,” Brandon said.

He added that the group intends to begin circulating a poll conducted last weekend by Frank Luntz showing that tea partiers could still be convinced to start a third party if the GOP doesn’t rededicate itself to small government principles.

The poll found 58 percent of the nearly 1,200 respondents – and nearly 79 percent of a smaller tea party sample – said they would consider “supporting the creation of a new third party dedicated to reducing the size and scope of Washington” if “a new Republican majority fails to deliver on their promises.”

“Given this new data, the tea party is just as viable as the Republican and Democratic parties. It’s vibrant, it’s sustainable, and it is not going anywhere,” said Luntz, an architect of the 1994 GOP takeover of Congress.

But Ned Ryun, president of a non-profit group called American Majority, which trains tea party candidates and activists, said the movement needs more organization, funding and focus to develop the infrastructure necessary to become a sustainable force in politics.

“They need to, in a systematic way, create a farm team, a bench, of effective and authentic conservative leaders at the state and local level – anything from school board to city council and county commission,” said Ryun, who lamented that some 2010 tea party candidates, including O’Donnell, were able to win tea party support simply because activists lacked alternatives.

Ryun’s group plans to announce a new training initiative later this month, and he told POLITICO that local tea party organizers would be wise to focus on “voter registration, and to work to hardwire their precincts and neighborhoods, so that they can become a real political machine that can turn out the vote, in 2011 and 2012.”

But Andrew Ian Dodge, the Maine state coordinator for the influential Tea Party Patriots umbrella coalition of local groups, said the electoral focus of many national tea party groups could diminish the movement’s ability to be a force in policy fights in the coming congress.

“I think the tea party groups that set themselves out as more issues-based and more policy-based are going to survive, while the ones that were more electorally based – basically Republican fronts – are probably going to disappear because they’ll be exhausted and burnt out from the cult-like way they’ve thrown themselves into it, or they’ll become disillusioned very quickly” with the legislative process.

Either way, Dodge said, the next few months will be critical in determining the future of the movement. “I have no idea what the tea party movement is going to look like on April 15, 2011, and I don’t’ think anyone does. Anybody who says they do is full of it.”